Question: $h(t) = -5t^{2}+5(g(t))$ $g(x) = x$ $ h(g(-8)) = {?} $
Solution: First, let's solve for the value of the inner function, $g(-8)$ . Then we'll know what to plug into the outer function. $g(-8) = -8$ $g(-8) = -8$ Now we know that $g(-8) = -8$ . Let's solve for $h(g(-8))$ , which is $h(-8)$ $h(-8) = -5(-8)^{2}+5(g(-8))$ To solve for the value of $h$ , we need to solve for the value of $g(-8)$ $g(-8) = -8$ $g(-8) = -8$ That means $h(-8) = -5(-8)^{2}+(5)(-8)$ $h(-8) = -360$